تكلم مع الذكاء الاصطناعي
Deck 4: Exponential and Logarithmic Functions
ملء الشاشة (f)
سؤال
Determine whether the function has an inverse function, If it does, find its inverse function. 
A) No,
does not have an inverse function.
B) Yes,
has an inverse function, 
C) Yes,
has an inverse function, 
D) Yes,
has an inverse function, 
E) Yes,
has an inverse function, 
A) No,
does not have an inverse function.B) Yes,
has an inverse function, C) Yes,
has an inverse function, D) Yes,
has an inverse function, E) Yes,
has an inverse function, 
سؤال
The demand function for a limited edition comic book is given by 
Find the price 
for a demand of 
units.
A) $5789.56
B) $258.96
C) $312.99
D) $6312.99
E) $210.44
Find the price for a demand of units.A) $5789.56
B) $258.96
C) $312.99
D) $6312.99
E) $210.44
سؤال
Evaluate the expression below.Round your results to three decimal places. 
A) 0.135
B) 0.018
C) 54.598
D) 0.050
E) 0.007
A) 0.135
B) 0.018
C) 54.598
D) 0.050
E) 0.007
سؤال
Determine whether the function has an inverse function, If it does, find its inverse function. 
A) No,
does not have an inverse function.
B) Yes,
has an inverse function, 
C) Yes,
has an inverse function, 
D) Yes,
has an inverse function, 
E) Yes,
has an inverse function, 
A) No,
does not have an inverse function.B) Yes,
has an inverse function, C) Yes,
has an inverse function, D) Yes,
has an inverse function, E) Yes,
has an inverse function, سؤال
Use the functions given by 
and 
to find the composition of functions 
A)
B)
C)
D)
E)
and to find the composition of functions A)
B)
C)
D)
E)
سؤال
Use the graph of 
to determine whether the function has an inverse function. 
A) Yes,
has an inverse function.
B) No,
does not have an inverse function.
to determine whether the function has an inverse function. A) Yes,
has an inverse function.B) No,
does not have an inverse function. سؤال
A company's profit 
for producing 
units is given by 
Find the inverse function 
and explain what it represents.Describe the domains of 
and 
A)
, 
represents the number of units that must be sold to obtain the profit of 
Domain of 
, Domain of 
B)
, 
represents the number of units that must be sold to obtain the profit of 
Domain of 
, Domain of 
C)
, 
represents the number of units that must be sold to obtain the profit of 
Domain of 
, Domain of 
D)
, 
represents the number of units that must be sold to obtain the profit of 
Domain of 
, Domain of 
E)
, 
represents the number of units that must be sold to obtain the profit of 
Domain of 
, Domain of 
for producing units is given by Find the inverse function and explain what it represents.Describe the domains of and A)
, represents the number of units that must be sold to obtain the profit of Domain of , Domain of B)
, represents the number of units that must be sold to obtain the profit of Domain of , Domain of C)
, represents the number of units that must be sold to obtain the profit of Domain of , Domain of D)
, represents the number of units that must be sold to obtain the profit of Domain of , Domain of E)
, represents the number of units that must be sold to obtain the profit of Domain of , Domain of سؤال
Use the functions given by 
and 
to find the value 
A) 1
B) 0
C) 3
D) 4
E) 2
and to find the value A) 1
B) 0
C) 3
D) 4
E) 2
سؤال
Sketch the graph of the function 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
Use the graph of 
to determine whether the function has an inverse function. 
A) No,
does not have an inverse function.
B) Yes,
has an inverse function.
to determine whether the function has an inverse function. A) No,
does not have an inverse function.B) Yes,
has an inverse function. سؤال
Use the functions given by 
and 
to find the value 
A) 16
B) -16
C) 32
D) The value does not exist.
E) -32
and to find the value A) 16
B) -16
C) 32
D) The value does not exist.
E) -32
سؤال
Find the inverse function informally 
Verify that 
and 
A)
, 
, 
B)
, 
, 
C)
, 
, 
D)
, 
, 
E)
, 
, 
Verify that and A)
, , B)
, , C)
, , D)
, , E)
, , سؤال
Use the functions given by 
and 
to find the composition of functions 
A)
B)
C)
D)
E)
and to find the composition of functions A)
B)
C)
D)
E)
سؤال
Use the functions given by 
and 
to find the value 
A) 32
B) 35
C) 33
D) 37
E) 30
and to find the value A) 32
B) 35
C) 33
D) 37
E) 30
سؤال
Show that 
and 
are functions by using the definition of inverse functions. 
A)
B)
C)
D)
E)
and are functions by using the definition of inverse functions. A)
B)
C)
D)
E)
سؤال
Show that 
and 
are functions by using the definition of inverse functions. 
A)
B)
C)
D)
E)
and are functions by using the definition of inverse functions. A)
B)
C)
D)
E)
سؤال
Find the inverse function of the function f given by the set of ordered pairs. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
Determine which of the following functions is graphed below. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
Find the inverse function informally 
Verify that 
and 
A)
, 
, 
B)
, 
, 
C)
, 
, 
D)
, 
, 
E)
, 
, 
Verify that and A)
, , B)
, , C)
, , D)
, , E)
, , سؤال
Find the inverse function of the function f given by the set of ordered pairs. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
Sketch the graph of the function 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
Write the logarithmic equation 
in its exponential form.
A)
B)
C)
D)
E)
in its exponential form.A)
B)
C)
D)
E)
سؤال
Match the function 
with its graph.
A)
B)
C)
D)
E)
with its graph.A)
B)
C)
D)
E)
سؤال
Find the vertical asymptote of the logarithmic function below. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
Evaluate the logarithm 
without using a calculator.
A)
B)
C)
D)
E)
without using a calculator.A)
B)
C)
D)
E)
سؤال
Use a calculator to evaluate 
Round your result to three decimal places.
A)
B)
C)
D)
E)
Round your result to three decimal places.A)
B)
C)
D)
E)
سؤال
Sketch the graph of the function 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
Match the function below with its graph. 
Graph I : 
Graph IV: 
Graph II: 
Graph V: 
Graph III: 
A) Graph II
B) Graph V
C) Graph I
D) Graph IV
E) Graph III
Graph I : Graph IV: Graph II: Graph V: Graph III: A) Graph II
B) Graph V
C) Graph I
D) Graph IV
E) Graph III
سؤال
Sketch the graph of the function 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
Use a calculator to evaluate 
Round your result to three decimal places.
A)
B)
C)
D)
E)
Round your result to three decimal places.A)
B)
C)
D)
E)
سؤال
Rewrite the logarithmic equation 
in exponential form.
A)
B)
C)
D)
E)
in exponential form.A)
B)
C)
D)
E)
سؤال
Use a calculator to evaluate the function 
for the given value of 
, 
Round your result to three decimal places.
A)
B)
C)
D)
E)
for the given value of , Round your result to three decimal places.A)
B)
C)
D)
E)
سؤال
Use a calculator to evaluate the function 
for the given value of 
, 
Round your result to three decimal places.
A)
B)
C)
D)
E)
for the given value of , Round your result to three decimal places.A)
B)
C)
D)
E)
سؤال
Write the logarithmic equation 
in exponential form.
A)
B)
C)
D)
E)
in exponential form.A)
B)
C)
D)
E)
سؤال
Sketch the graph of the function 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
Rewrite the exponential equation 
in logarithmic form.
A)
B)
C)
D)
E)
in logarithmic form.A)
B)
C)
D)
E)
سؤال
Find the domain of the function 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
Write the exponential equation 
in its logarithmic form.
A)
B)
C)
D)
E)
in its logarithmic form.A)
B)
C)
D)
E)
سؤال
Write the exponential equation 
in logarithmic form.
A)
B)
C)
D)
E)
in logarithmic form.A)
B)
C)
D)
E)
سؤال
Match the function 
with its graph.
A)
B)
C)
D)
E)
with its graph.A)
B)
C)
D)
E)
سؤال
Write 
as a single logarithm with a coefficient of 1. Assume all variable expressions represent positive real numbers.
A)
B)
C)
D)
E)
as a single logarithm with a coefficient of 1. Assume all variable expressions represent positive real numbers.A)
B)
C)
D)
E)
سؤال
Expand the logarithmic expression 
Assume all variable expressions represent positive real numbers.
A)
B)
C)
D)
E)
Assume all variable expressions represent positive real numbers.A)
B)
C)
D)
E)
سؤال
Solve for x. 
A)
B)
C)
D)
E) 2
A)
B)
C)
D)
E) 2
سؤال
The present value of money is the principal 
you need to invest today so that it will grow to an amount 
at the end of specified time.The present value formula 
is obtained by solving the compound interest formula 
for 
Recall that 
is the number of years, 
is the interest rate per year, and 
is the number of compoundings per year.find the present value of amount 
invested at rate 
for 
years, compounded 
times per year. 
A)
B)
C)
D)
E)
you need to invest today so that it will grow to an amount at the end of specified time.The present value formula is obtained by solving the compound interest formula for Recall that is the number of years, is the interest rate per year, and is the number of compoundings per year.find the present value of amount invested at rate for years, compounded times per year. A)
B)
C)
D)
E)
سؤال
Approximate the logarithm below using the properties of logarithms, given 
and 
A) -0.2084
B) 0.2625
C) -0.4709
D) -0.2625
E) 0.4709
and A) -0.2084
B) 0.2625
C) -0.4709
D) -0.2625
E) 0.4709
سؤال
Find the exact value of 
without using a calculator.
A)
B)
C)
D)
E) -1
without using a calculator.A)
B)
C)
D)
E) -1
سؤال
Evaluate the logarithm 
using the change of base formula.Round to 3 decimal places.
A) 6.303
B) 0.309
C) 3.239
D) 12.264
E) 2.737
using the change of base formula.Round to 3 decimal places.A) 6.303
B) 0.309
C) 3.239
D) 12.264
E) 2.737
سؤال
Condense the expression 
to the logarithm of a single term.
A)
B)
C)
D)
E)
to the logarithm of a single term.A)
B)
C)
D)
E)
سؤال
Use the properties of logarithms to simplify the logarithmic expression below. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
Expand the given logarithmic expression.Assume all variable expressions represent positive real numbers. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
The demand function for a home theater system is given by 
a)Find the price p for a demand of x=200 units. b)Find the price p for a demand of x=900 units.
C)Use a graphing utility to graph the demand function.
D)Use the graph from part (c) to approximate the demand when the price is $400.
A) a)$435.23.
B)$45.78.
C)
D)$320.9
B) a)$545.26.
B)$71.32.
C)
D)$310.16
C) a)$573.26.
B)$34.98.
C)
D)$450.00
D) a)$345
B)$49.90.
C)
D)$542.00
E) a)$465.56.
B)$65.89.
C)
D)$359.78
a)Find the price p for a demand of x=200 units. b)Find the price p for a demand of x=900 units.C)Use a graphing utility to graph the demand function.
D)Use the graph from part (c) to approximate the demand when the price is $400.
A) a)$435.23.
B)$45.78.
C)
D)$320.9
B) a)$545.26.
B)$71.32.
C)
D)$310.16
C) a)$573.26.
B)$34.98.
C)
D)$450.00
D) a)$345
B)$49.90.
C)
D)$542.00
E) a)$465.56.
B)$65.89.
C)
D)$359.78
سؤال
You deposit a lump sum 
in a trust fund on the day your child is born.The fund earns 6.5% interest compounded continuously.Find the amount 
that will yield the given balance 
on your child's 25th birthday. 
A)
B)
C)
D)
E)
in a trust fund on the day your child is born.The fund earns 6.5% interest compounded continuously.Find the amount that will yield the given balance on your child's 25th birthday. A)
B)
C)
D)
E)
سؤال
Condense the expression 
to the logarithm of a single term.
A)
B)
C)
D)
E)
to the logarithm of a single term.A)
B)
C)
D)
E)
سؤال
The number of certain type of bacteria increases according to the model 
where t is time (in hours) a)Find P(0).
B)Find P(5).
C)Find P(10).
D)Find P(24).
A) a)
B)
C)
D)
B) a)
B)
C)
D)
C) a)
B)
C)
D)
D) a)
B)
C)
D)
E) a)
B)
C)
D)
where t is time (in hours) a)Find P(0).B)Find P(5).
C)Find P(10).
D)Find P(24).
A) a)
B)
C)
D)
B) a)
B)
C)
D)
C) a)
B)
C)
D)
D) a)
B)
C)
D)
E) a)
B)
C)
D)
سؤال
Write the expression below as a single logarithm with a coefficient of 1.Assume all variable expressions represent positive real numbers. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
The present value of money is the principal 
you need to invest today so that it will grow to an amount 
at the end of specified time.The present value formula 
is obtained by solving the compound interest formula 
for 
Recall that 
is the number of years, 
is the interest rate per year, and 
is the number of compoundings per year.find the present value of amount 
invested at rate 
for 
years, compounded 
times per year. 
A)
B)
C)
D)
E)
you need to invest today so that it will grow to an amount at the end of specified time.The present value formula is obtained by solving the compound interest formula for Recall that is the number of years, is the interest rate per year, and is the number of compoundings per year.find the present value of amount invested at rate for years, compounded times per year. A)
B)
C)
D)
E)
سؤال
Strontinum-90 has a half life of 29.1 years.The amount S of 100 kilograms of Strontinum6990 present after t years is given by 
How much of the 100 kilograms will remain after 50 years?
A) about 31.4 kilograms
B) about 35.4 kilograms
C) about 30.4 kilograms
D) about 37.4 kilograms
E) about 40.4 kilograms
How much of the 100 kilograms will remain after 50 years?A) about 31.4 kilograms
B) about 35.4 kilograms
C) about 30.4 kilograms
D) about 37.4 kilograms
E) about 40.4 kilograms
سؤال
The approximate lengths and diameters (in inches) of common nails are shown in the table.Find a logarithmic equation that relates the diameter 
of a common nail to its length 
A)
B)
C)
D)
E)
of a common nail to its length A)
B)
C)
D)
E)
سؤال
Determine whether 
Justify your answer.
A) Yes,
because 
is a rational number.
B) No,
because 
is not a rational number.
Justify your answer.A) Yes,
because is a rational number.B) No,
because is not a rational number. سؤال
The U.S.annual gross domestic product G (in billions of dollars) from 1985 through 2009 can be modeled by 
where 
represents the year, with 
corresponding to 1985 (Source: U.S.Bureau of Economics Analysis) (a) Use a graphing utility to graph G for the years 1985 through 2009.
(b) Use the graph from part (a) to estimate the gross domestic product in 1990,2000 and 2009.
A) a.
B) 1990: $5682.8 billion
2000: $4624.6 billion
2009: $15,463.8 billion
B) a.
B) 1990: $5682.8 billion
2000: $9624.6 billion
2009: $10,463.8 billion
C) a.
B) 1990: $5682.8 billion
2000: $9624.6 billion
2009: $15,463.8 billion
D) a.
B) 1990: $682.8 billion
2000: $9624.6 billion
2009: $15,463.8 billion
E) a.
B) 1990: $5682.8 billion
2000: $624.6 billion
2009: $15,463.8 billion
where represents the year, with corresponding to 1985 (Source: U.S.Bureau of Economics Analysis) (a) Use a graphing utility to graph G for the years 1985 through 2009.(b) Use the graph from part (a) to estimate the gross domestic product in 1990,2000 and 2009.
A) a.
B) 1990: $5682.8 billion
2000: $4624.6 billion
2009: $15,463.8 billion
B) a.
B) 1990: $5682.8 billion
2000: $9624.6 billion
2009: $10,463.8 billion
C) a.
B) 1990: $5682.8 billion
2000: $9624.6 billion
2009: $15,463.8 billion
D) a.
B) 1990: $682.8 billion
2000: $9624.6 billion
2009: $15,463.8 billion
E) a.
B) 1990: $5682.8 billion
2000: $624.6 billion
2009: $15,463.8 billion
سؤال
The average monthly sales 
(in billions of dollars) in retail trade in the United States from 1996 to 2005 can be approximated by the model 
where 
represents the year, with 
corresponding to 1996.Estimate the year in which the average monthly sales first exceeded $330 billion.
A) 2003
B) 2004
C) 2002
D) 1999
E) 1997
(in billions of dollars) in retail trade in the United States from 1996 to 2005 can be approximated by the model where represents the year, with corresponding to 1996.Estimate the year in which the average monthly sales first exceeded $330 billion.A) 2003
B) 2004
C) 2002
D) 1999
E) 1997
سؤال
سؤال
Solve for x: 
Round to 3 decimal places.
A) 1.407
B) 0.407
C) 1.362
D) -1.362
E) no solution
Round to 3 decimal places.A) 1.407
B) 0.407
C) 1.362
D) -1.362
E) no solution
سؤال
سؤال
Approximate the solution to 
Round to 3 decimal places.
A) -0.632
B) 0.500
C) 0.582
D) 2.718
E) 0.111
Round to 3 decimal places.A) -0.632
B) 0.500
C) 0.582
D) 2.718
E) 0.111
سؤال
Solve for x: 
Round to 3 decimal places.
A) 9.803
B) 15.777
C) 20.606
D) -20.606
E) -3.268
Round to 3 decimal places.A) 9.803
B) 15.777
C) 20.606
D) -20.606
E) -3.268
سؤال
Solve for 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
Use algebraic procedures to find the exact solution of the equation 
A) 0, -2
B) 4
C) 3, 2
D) -2, 4
E) 2
A) 0, -2
B) 4
C) 3, 2
D) -2, 4
E) 2
سؤال
Approximate the solution of 
to 3 decimal places.(You may use a graphing utility.)
A) -3.329
B) -0.299
C) -1.427
D) -0.986
E) -0.110
to 3 decimal places.(You may use a graphing utility.)A) -3.329
B) -0.299
C) -1.427
D) -0.986
E) -0.110
سؤال
Use algebraic procedures to find the exact solution(s) of the equation below. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
Apply the Inverse Property of logarithmic or exponential functions to simplify the expression below. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
Solve 
for x.
A) 1
B)
C)
D)
E) no solution
for x.A) 1
B)
C)
D)
E) no solution
سؤال
Use algebraic procedures to find the exact solution(s) of the equation below. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
An industrial psychologist has determined that the average percent score for an employee on a test of the employee's knowledge of the company's product is given by 
where t is the number of weeks on the job and P is the percent score.Estimate (to the nearest week) the expected number of weeks of employment that are necessary for an employee to earn a 90% score on the test.
A) 5 weeks
B) 50 weeks
C) 29 weeks
D) 43 weeks
E) 25 weeks
where t is the number of weeks on the job and P is the percent score.Estimate (to the nearest week) the expected number of weeks of employment that are necessary for an employee to earn a 90% score on the test.A) 5 weeks
B) 50 weeks
C) 29 weeks
D) 43 weeks
E) 25 weeks
سؤال
Solve the exponential equation algebraically.Approximate the result to three decimal places. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
Use a graphing utility to approximate the solution to 
Round to 3 decimal places.
A) 3.702
B) 2.702
C) 1.851
D) 1.351
E) no solution
Round to 3 decimal places.A) 3.702
B) 2.702
C) 1.851
D) 1.351
E) no solution
سؤال
Use algebraic procedures to find the exact solution of the equation 
A) -1, 7
B)
C) 2, 3
D) 7
E) 1
A) -1, 7
B)
C) 2, 3
D) 7
E) 1
سؤال
سؤال
Approximate the solution to 
Round to 3 decimal places.
A) 2.226
B) 6.133
C) 4.586
D) -0.223
E) 396.223
Round to 3 decimal places.A) 2.226
B) 6.133
C) 4.586
D) -0.223
E) 396.223
سؤال
Solve the exponential equation algebraically.Approximate the result to three decimal places. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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ملء الشاشة (f)
Deck 4: Exponential and Logarithmic Functions
1
Determine whether the function has an inverse function, If it does, find its inverse function.
A) No, does not have an inverse function.
B) Yes, has an inverse function,
C) Yes, has an inverse function,
D) Yes, has an inverse function,
E) Yes, has an inverse function,
A) No,
does not have an inverse function.B) Yes,
has an inverse function, C) Yes,
has an inverse function, D) Yes,
has an inverse function, E) Yes,
has an inverse function, A
2
The demand function for a limited edition comic book is given by Find the price for a demand of units.
A) $5789.56
B) $258.96
C) $312.99
D) $6312.99
E) $210.44
Find the price for a demand of units.A) $5789.56
B) $258.96
C) $312.99
D) $6312.99
E) $210.44
B
3
Evaluate the expression below.Round your results to three decimal places.
A) 0.135
B) 0.018
C) 54.598
D) 0.050
E) 0.007
A) 0.135
B) 0.018
C) 54.598
D) 0.050
E) 0.007
B
4
Determine whether the function has an inverse function, If it does, find its inverse function.
A) No, does not have an inverse function.
B) Yes, has an inverse function,
C) Yes, has an inverse function,
D) Yes, has an inverse function,
E) Yes, has an inverse function,
A) No,
does not have an inverse function.B) Yes,
has an inverse function, C) Yes,
has an inverse function, D) Yes,
has an inverse function, E) Yes,
has an inverse function, فتح الحزمة
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5
Use the functions given by and to find the composition of functions
A)
B)
C)
D)
E)
and to find the composition of functions A)
B)
C)
D)
E)
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6
Use the graph of to determine whether the function has an inverse function.
A) Yes, has an inverse function.
B) No, does not have an inverse function.
to determine whether the function has an inverse function. A) Yes,
has an inverse function.B) No,
does not have an inverse function. فتح الحزمة
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7
A company's profit for producing units is given by Find the inverse function and explain what it represents.Describe the domains of and
A) , represents the number of units that must be sold to obtain the profit of Domain of , Domain of
B) , represents the number of units that must be sold to obtain the profit of Domain of , Domain of
C) , represents the number of units that must be sold to obtain the profit of Domain of , Domain of
D) , represents the number of units that must be sold to obtain the profit of Domain of , Domain of
E) , represents the number of units that must be sold to obtain the profit of Domain of , Domain of
for producing units is given by Find the inverse function and explain what it represents.Describe the domains of and A)
, represents the number of units that must be sold to obtain the profit of Domain of , Domain of B)
, represents the number of units that must be sold to obtain the profit of Domain of , Domain of C)
, represents the number of units that must be sold to obtain the profit of Domain of , Domain of D)
, represents the number of units that must be sold to obtain the profit of Domain of , Domain of E)
, represents the number of units that must be sold to obtain the profit of Domain of , Domain of فتح الحزمة
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8
Use the functions given by and to find the value
A) 1
B) 0
C) 3
D) 4
E) 2
and to find the value A) 1
B) 0
C) 3
D) 4
E) 2
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9
Sketch the graph of the function
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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10
Use the graph of to determine whether the function has an inverse function.
A) No, does not have an inverse function.
B) Yes, has an inverse function.
to determine whether the function has an inverse function. A) No,
does not have an inverse function.B) Yes,
has an inverse function. فتح الحزمة
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11
Use the functions given by and to find the value
A) 16
B) -16
C) 32
D) The value does not exist.
E) -32
and to find the value A) 16
B) -16
C) 32
D) The value does not exist.
E) -32
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12
Find the inverse function informally Verify that and
A) , ,
B) , ,
C) , ,
D) , ,
E) , ,
Verify that and A)
, , B)
, , C)
, , D)
, , E)
, , فتح الحزمة
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13
Use the functions given by and to find the composition of functions
A)
B)
C)
D)
E)
and to find the composition of functions A)
B)
C)
D)
E)
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14
Use the functions given by and to find the value
A) 32
B) 35
C) 33
D) 37
E) 30
and to find the value A) 32
B) 35
C) 33
D) 37
E) 30
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15
Show that and are functions by using the definition of inverse functions.
A)
B)
C)
D)
E)
and are functions by using the definition of inverse functions. A)
B)
C)
D)
E)
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16
Show that and are functions by using the definition of inverse functions.
A)
B)
C)
D)
E)
and are functions by using the definition of inverse functions. A)
B)
C)
D)
E)
فتح الحزمة
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17
Find the inverse function of the function f given by the set of ordered pairs.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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18
Determine which of the following functions is graphed below.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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19
Find the inverse function informally Verify that and
A) , ,
B) , ,
C) , ,
D) , ,
E) , ,
Verify that and A)
, , B)
, , C)
, , D)
, , E)
, , فتح الحزمة
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20
Find the inverse function of the function f given by the set of ordered pairs.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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21
Sketch the graph of the function
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
فتح الحزمة
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22
Write the logarithmic equation in its exponential form.
A)
B)
C)
D)
E)
in its exponential form.A)
B)
C)
D)
E)
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23
Match the function with its graph.
A)
B)
C)
D)
E)
with its graph.A)
B)
C)
D)
E)
فتح الحزمة
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24
Find the vertical asymptote of the logarithmic function below.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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25
Evaluate the logarithm without using a calculator.
A)
B)
C)
D)
E)
without using a calculator.A)
B)
C)
D)
E)
فتح الحزمة
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26
Use a calculator to evaluate Round your result to three decimal places.
A)
B)
C)
D)
E)
Round your result to three decimal places.A)
B)
C)
D)
E)
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27
Sketch the graph of the function
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
فتح الحزمة
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28
Match the function below with its graph. Graph I : Graph IV: Graph II: Graph V: Graph III:
A) Graph II
B) Graph V
C) Graph I
D) Graph IV
E) Graph III
Graph I : Graph IV: Graph II: Graph V: Graph III: A) Graph II
B) Graph V
C) Graph I
D) Graph IV
E) Graph III
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29
Sketch the graph of the function
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
فتح الحزمة
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30
Use a calculator to evaluate Round your result to three decimal places.
A)
B)
C)
D)
E)
Round your result to three decimal places.A)
B)
C)
D)
E)
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31
Rewrite the logarithmic equation in exponential form.
A)
B)
C)
D)
E)
in exponential form.A)
B)
C)
D)
E)
فتح الحزمة
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32
Use a calculator to evaluate the function for the given value of , Round your result to three decimal places.
A)
B)
C)
D)
E)
for the given value of , Round your result to three decimal places.A)
B)
C)
D)
E)
فتح الحزمة
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33
Use a calculator to evaluate the function for the given value of , Round your result to three decimal places.
A)
B)
C)
D)
E)
for the given value of , Round your result to three decimal places.A)
B)
C)
D)
E)
فتح الحزمة
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34
Write the logarithmic equation in exponential form.
A)
B)
C)
D)
E)
in exponential form.A)
B)
C)
D)
E)
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35
Sketch the graph of the function
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
فتح الحزمة
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36
Rewrite the exponential equation in logarithmic form.
A)
B)
C)
D)
E)
in logarithmic form.A)
B)
C)
D)
E)
فتح الحزمة
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37
Find the domain of the function
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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38
Write the exponential equation in its logarithmic form.
A)
B)
C)
D)
E)
in its logarithmic form.A)
B)
C)
D)
E)
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39
Write the exponential equation in logarithmic form.
A)
B)
C)
D)
E)
in logarithmic form.A)
B)
C)
D)
E)
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40
Match the function with its graph.
A)
B)
C)
D)
E)
with its graph.A)
B)
C)
D)
E)
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41
Write as a single logarithm with a coefficient of 1. Assume all variable expressions represent positive real numbers.
A)
B)
C)
D)
E)
as a single logarithm with a coefficient of 1. Assume all variable expressions represent positive real numbers.A)
B)
C)
D)
E)
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42
Expand the logarithmic expression Assume all variable expressions represent positive real numbers.
A)
B)
C)
D)
E)
Assume all variable expressions represent positive real numbers.A)
B)
C)
D)
E)
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43
Solve for x.
A)
B)
C)
D)
E) 2
A)
B)
C)
D)
E) 2
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44
The present value of money is the principal you need to invest today so that it will grow to an amount at the end of specified time.The present value formula is obtained by solving the compound interest formula for Recall that is the number of years, is the interest rate per year, and is the number of compoundings per year.find the present value of amount invested at rate for years, compounded times per year.
A)
B)
C)
D)
E)
you need to invest today so that it will grow to an amount at the end of specified time.The present value formula is obtained by solving the compound interest formula for Recall that is the number of years, is the interest rate per year, and is the number of compoundings per year.find the present value of amount invested at rate for years, compounded times per year. A)
B)
C)
D)
E)
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45
Approximate the logarithm below using the properties of logarithms, given and
A) -0.2084
B) 0.2625
C) -0.4709
D) -0.2625
E) 0.4709
and A) -0.2084
B) 0.2625
C) -0.4709
D) -0.2625
E) 0.4709
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46
Find the exact value of without using a calculator.
A)
B)
C)
D)
E) -1
without using a calculator.A)
B)
C)
D)
E) -1
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47
Evaluate the logarithm using the change of base formula.Round to 3 decimal places.
A) 6.303
B) 0.309
C) 3.239
D) 12.264
E) 2.737
using the change of base formula.Round to 3 decimal places.A) 6.303
B) 0.309
C) 3.239
D) 12.264
E) 2.737
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48
Condense the expression to the logarithm of a single term.
A)
B)
C)
D)
E)
to the logarithm of a single term.A)
B)
C)
D)
E)
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49
Use the properties of logarithms to simplify the logarithmic expression below.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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50
Expand the given logarithmic expression.Assume all variable expressions represent positive real numbers.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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51
The demand function for a home theater system is given by a)Find the price p for a demand of x=200 units. b)Find the price p for a demand of x=900 units.
C)Use a graphing utility to graph the demand function.
D)Use the graph from part (c) to approximate the demand when the price is $400.
A) a)$435.23.
B)$45.78.
C)
D)$320.9
B) a)$545.26.
B)$71.32.
C)
D)$310.16
C) a)$573.26.
B)$34.98.
C)
D)$450.00
D) a)$345
B)$49.90.
C)
D)$542.00
E) a)$465.56.
B)$65.89.
C)
D)$359.78
a)Find the price p for a demand of x=200 units. b)Find the price p for a demand of x=900 units.C)Use a graphing utility to graph the demand function.
D)Use the graph from part (c) to approximate the demand when the price is $400.
A) a)$435.23.
B)$45.78.
C)
D)$320.9
B) a)$545.26.
B)$71.32.
C)
D)$310.16
C) a)$573.26.
B)$34.98.
C)
D)$450.00
D) a)$345
B)$49.90.
C)
D)$542.00
E) a)$465.56.
B)$65.89.
C)
D)$359.78
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52
You deposit a lump sum in a trust fund on the day your child is born.The fund earns 6.5% interest compounded continuously.Find the amount that will yield the given balance on your child's 25th birthday.
A)
B)
C)
D)
E)
in a trust fund on the day your child is born.The fund earns 6.5% interest compounded continuously.Find the amount that will yield the given balance on your child's 25th birthday. A)
B)
C)
D)
E)
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53
Condense the expression to the logarithm of a single term.
A)
B)
C)
D)
E)
to the logarithm of a single term.A)
B)
C)
D)
E)
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54
The number of certain type of bacteria increases according to the model where t is time (in hours) a)Find P(0).
B)Find P(5).
C)Find P(10).
D)Find P(24).
A) a)
B)
C)
D)
B) a)
B)
C)
D)
C) a)
B)
C)
D)
D) a)
B)
C)
D)
E) a)
B)
C)
D)
where t is time (in hours) a)Find P(0).B)Find P(5).
C)Find P(10).
D)Find P(24).
A) a)
B)
C)
D)
B) a)
B)
C)
D)
C) a)
B)
C)
D)
D) a)
B)
C)
D)
E) a)
B)
C)
D)
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55
Write the expression below as a single logarithm with a coefficient of 1.Assume all variable expressions represent positive real numbers.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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56
The present value of money is the principal you need to invest today so that it will grow to an amount at the end of specified time.The present value formula is obtained by solving the compound interest formula for Recall that is the number of years, is the interest rate per year, and is the number of compoundings per year.find the present value of amount invested at rate for years, compounded times per year.
A)
B)
C)
D)
E)
you need to invest today so that it will grow to an amount at the end of specified time.The present value formula is obtained by solving the compound interest formula for Recall that is the number of years, is the interest rate per year, and is the number of compoundings per year.find the present value of amount invested at rate for years, compounded times per year. A)
B)
C)
D)
E)
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57
Strontinum-90 has a half life of 29.1 years.The amount S of 100 kilograms of Strontinum6990 present after t years is given by How much of the 100 kilograms will remain after 50 years?
A) about 31.4 kilograms
B) about 35.4 kilograms
C) about 30.4 kilograms
D) about 37.4 kilograms
E) about 40.4 kilograms
How much of the 100 kilograms will remain after 50 years?A) about 31.4 kilograms
B) about 35.4 kilograms
C) about 30.4 kilograms
D) about 37.4 kilograms
E) about 40.4 kilograms
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58
The approximate lengths and diameters (in inches) of common nails are shown in the table.Find a logarithmic equation that relates the diameter of a common nail to its length
A)
B)
C)
D)
E)
of a common nail to its length A)
B)
C)
D)
E)
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59
Determine whether Justify your answer.
A) Yes, because is a rational number.
B) No, because is not a rational number.
Justify your answer.A) Yes,
because is a rational number.B) No,
because is not a rational number. فتح الحزمة
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60
The U.S.annual gross domestic product G (in billions of dollars) from 1985 through 2009 can be modeled by where represents the year, with corresponding to 1985 (Source: U.S.Bureau of Economics Analysis) (a) Use a graphing utility to graph G for the years 1985 through 2009.
(b) Use the graph from part (a) to estimate the gross domestic product in 1990,2000 and 2009.
A) a.
B) 1990: $5682.8 billion
2000: $4624.6 billion
2009: $15,463.8 billion
B) a.
B) 1990: $5682.8 billion
2000: $9624.6 billion
2009: $10,463.8 billion
C) a.
B) 1990: $5682.8 billion
2000: $9624.6 billion
2009: $15,463.8 billion
D) a.
B) 1990: $682.8 billion
2000: $9624.6 billion
2009: $15,463.8 billion
E) a.
B) 1990: $5682.8 billion
2000: $624.6 billion
2009: $15,463.8 billion
where represents the year, with corresponding to 1985 (Source: U.S.Bureau of Economics Analysis) (a) Use a graphing utility to graph G for the years 1985 through 2009.(b) Use the graph from part (a) to estimate the gross domestic product in 1990,2000 and 2009.
A) a.
B) 1990: $5682.8 billion
2000: $4624.6 billion
2009: $15,463.8 billion
B) a.
B) 1990: $5682.8 billion
2000: $9624.6 billion
2009: $10,463.8 billion
C) a.
B) 1990: $5682.8 billion
2000: $9624.6 billion
2009: $15,463.8 billion
D) a.
B) 1990: $682.8 billion
2000: $9624.6 billion
2009: $15,463.8 billion
E) a.
B) 1990: $5682.8 billion
2000: $624.6 billion
2009: $15,463.8 billion
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61
The average monthly sales (in billions of dollars) in retail trade in the United States from 1996 to 2005 can be approximated by the model where represents the year, with corresponding to 1996.Estimate the year in which the average monthly sales first exceeded $330 billion.
A) 2003
B) 2004
C) 2002
D) 1999
E) 1997
(in billions of dollars) in retail trade in the United States from 1996 to 2005 can be approximated by the model where represents the year, with corresponding to 1996.Estimate the year in which the average monthly sales first exceeded $330 billion.A) 2003
B) 2004
C) 2002
D) 1999
E) 1997
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62
Find the balance if $27,000 is invested at an annual rate of 6.5% for 4 years, compounded continuously.
A) $115,253.17
B) $34,020.00
C) $28,798.24
D) $20,818.39
E) $35,017.11
A) $115,253.17
B) $34,020.00
C) $28,798.24
D) $20,818.39
E) $35,017.11
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63
Solve for x: Round to 3 decimal places.
A) 1.407
B) 0.407
C) 1.362
D) -1.362
E) no solution
Round to 3 decimal places.A) 1.407
B) 0.407
C) 1.362
D) -1.362
E) no solution
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64
An initial investment of $6000 grows at an annual interest rate of 3% compounded continuously.How long will it take to double the investment?
A) 23.10 years
B) 24.10 years
C) 24.00 years
D) 23.00 years
E) 1 year
A) 23.10 years
B) 24.10 years
C) 24.00 years
D) 23.00 years
E) 1 year
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65
Approximate the solution to Round to 3 decimal places.
A) -0.632
B) 0.500
C) 0.582
D) 2.718
E) 0.111
Round to 3 decimal places.A) -0.632
B) 0.500
C) 0.582
D) 2.718
E) 0.111
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66
Solve for x: Round to 3 decimal places.
A) 9.803
B) 15.777
C) 20.606
D) -20.606
E) -3.268
Round to 3 decimal places.A) 9.803
B) 15.777
C) 20.606
D) -20.606
E) -3.268
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67
Solve for
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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68
Use algebraic procedures to find the exact solution of the equation
A) 0, -2
B) 4
C) 3, 2
D) -2, 4
E) 2
A) 0, -2
B) 4
C) 3, 2
D) -2, 4
E) 2
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69
Approximate the solution of to 3 decimal places.(You may use a graphing utility.)
A) -3.329
B) -0.299
C) -1.427
D) -0.986
E) -0.110
to 3 decimal places.(You may use a graphing utility.)A) -3.329
B) -0.299
C) -1.427
D) -0.986
E) -0.110
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70
Use algebraic procedures to find the exact solution(s) of the equation below.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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71
Apply the Inverse Property of logarithmic or exponential functions to simplify the expression below.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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72
Solve for x.
A) 1
B)
C)
D)
E) no solution
for x.A) 1
B)
C)
D)
E) no solution
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73
Use algebraic procedures to find the exact solution(s) of the equation below.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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74
An industrial psychologist has determined that the average percent score for an employee on a test of the employee's knowledge of the company's product is given by where t is the number of weeks on the job and P is the percent score.Estimate (to the nearest week) the expected number of weeks of employment that are necessary for an employee to earn a 90% score on the test.
A) 5 weeks
B) 50 weeks
C) 29 weeks
D) 43 weeks
E) 25 weeks
where t is the number of weeks on the job and P is the percent score.Estimate (to the nearest week) the expected number of weeks of employment that are necessary for an employee to earn a 90% score on the test.A) 5 weeks
B) 50 weeks
C) 29 weeks
D) 43 weeks
E) 25 weeks
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75
Solve the exponential equation algebraically.Approximate the result to three decimal places.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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76
Use a graphing utility to approximate the solution to Round to 3 decimal places.
A) 3.702
B) 2.702
C) 1.851
D) 1.351
E) no solution
Round to 3 decimal places.A) 3.702
B) 2.702
C) 1.851
D) 1.351
E) no solution
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77
Use algebraic procedures to find the exact solution of the equation
A) -1, 7
B)
C) 2, 3
D) 7
E) 1
A) -1, 7
B)
C) 2, 3
D) 7
E) 1
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78
How long will it take $10,000 to quadruple if it is invested in a savings account that pays 5.5% annual interest compounded continuously? Round to the nearest year.
A) 25 years
B) 20 years
C) 19 years
D) 32 years
E) 30 years
A) 25 years
B) 20 years
C) 19 years
D) 32 years
E) 30 years
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79
Approximate the solution to Round to 3 decimal places.
A) 2.226
B) 6.133
C) 4.586
D) -0.223
E) 396.223
Round to 3 decimal places.A) 2.226
B) 6.133
C) 4.586
D) -0.223
E) 396.223
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80
Solve the exponential equation algebraically.Approximate the result to three decimal places.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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